This disclosure relates generally to methods of optimizing designs, and more specifically to methods for designing structures that are optimized for manufacture with additive manufacturing processes.
Additive manufacturing (AM) processes are processes for fabricating parts through material addition. Specifically, AM devices manufacture three-dimensional objects by adding layer-upon-layer of material in the “build direction” (e.g., from the bottom to the top of the object). The growing interest in AM stems from its ability to fabricate highly complex parts with relative ease. However, structures built with AM must observe certain limitations of the AM processes. Polymer AM processes work with melted, partially melted, and/or amorphous materials, and unsolidified portions of layers can droop or creep where there is no underlying material providing support. The same “overhanging” portions can be damaged by burning during metal AM processes. Thus, overhanging portions of the structure require support structures to hold the overhanging portions in place during manufacture. These support structures are “sacrificial”—they are made of the same material as the structure being manufactured, and are removed after fabrication.
Support structures directly add to the build-time and material cost. Material costs can be substantial in AM; for example, the largest percentage cost for metal AM, besides the machine cost that is amortized, is material cost (18%). Further, support structures can be hard to remove (and sometimes even inaccessible), leading to the post-fabrication (clean-up) cost. Post-fabrication costs make-up for about 8% of AM product cost.
Topology optimization (TO) represents a class of computational methods for designing lightweight, high-performance structures. After several years of intensive research, it has emerged as a powerful design tool, and is deployed in optimization of aircraft components, spacecraft modules, automobile components, cast components, compliant mechanisms, etc. The overarching goal of TO is to start with a given design that meets specifications for rigidity, load bearing, force resistance, etc., and reduce it to an optimized design that is lighter in weight and uses the least amount of material while meeting the same specifications. Designs stemming from TO are geometrically complex, and therefore hard to manufacture using traditional processes, but these designs can often be additively manufactured. Also, since fabrication cost in AM is proportional to the material used, light-weight topology optimized designs are particularly relevant in AM. In theory, these and other characteristics make TO and AM well suited for each other. However, in practice, topologically optimized designs are often not AM friendly. One drawback is that TO processes, seeking the lightest-weight solution, create structures with many overhanging portions; this drives up the manufacturing costs due to the additional support structures needed.
Imposing manufacturing constraints in TO has been addressed before; a particularly relevant constraint is that of ‘draw-direction constraint’ for casting, where the TO algorithm was modified so as to avoid ‘inserts’. While this is analogous to the support structure constraint, there are two fundamental differences: (1) support structures are governed by a threshold angle, while the threshold angle for draw-direction is essentially zero, and (2) the draw-direction constraint is bidirectional, while the build-direction in AM is unidirectional. Thus, the draw-direction methodology does not apply to AM; novel methods are needed.
One approach to minimizing support structures proposes a penalization scheme on overhanging surfaces, and an edge analysis was carried out on a benchmark 2D example. The overhang constraint was suggested but not demonstrated. Another approach proposed a novel strategy to reduce the material cost by first extracting the frame structure of the design. However, the frame is in fact the solution of a multi-objective TO problem that minimizes the number of struts while considering stability and printability. Another proposal introduced the idea of self-supporting designs, where the TO optimized design was altered to include features similar to support structures. In other words, support structures were introduced as design features a posteriori. Since this is carried out after TO, the structural load path is altered, and may violate stress and other performance constraints.
Recently, another approach employed a smooth Heaviside approximation to penalize overhanging surfaces within a Solid Isotropic Material with Penalization (SIMP)-based TO. The approach demonstrated that, for 2D compliance minimization, this scheme changes the topology to be AM friendly. Specifically, it is possible to eliminate support structures by suitably changing the TO process. The results are encouraging, but there arose convergence issues when the overhanging penalization was imposed. A contemporaneous approach proposed a shape optimization technique to alter the model to a more self-supported one. To this end, once a volumetric tetrahedral mesh is generated, the overhang tetrahedra are mapped onto the Gauss sphere and minimally rotated to a self-supported state.
While there have been some significant research activities in TO and AM, a robust framework for integrating the two is lacking. Therefore, the purpose of this disclosure is to provide a TO methodology for limiting the support structure volume, thereby leading to designs that are AM friendly.